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Chapter 5
Multiple Regression
Multiple regression is a standard statistical technique by which one or
more independent variables are used to predict a single dependent
variable. For example, we may have n independent variables, X
lf
X
2
, ..., X
n
and a dependent variable Y. Given many n + 1 long vectors
of observed values for these n + 1 variables, the goal of multiple
regression is to find values for n + 1 coefficients, a
if
i=0, ..., n, such
that we can predict Y from given X values:
n
y
= a
o
+
Σ
a
i
x
i
5
"
3
The coefficients are traditionally chosen such that the sum of the
squared error for all training samples is minimized. There are severa